This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for some (...) countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is countable, (...) the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π12 comprehension. An MF space is defined to be a topological space of the form MF with the topology generated by {Np ∣ p ϵ P}. Here P is a poset, MF is the set of maximal filters on P, and Np = {F ϵ MF ∣ p ϵ F }. If the poset P is countable, the space MF is said to (...) be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to. The equivalence is proved in the weaker system. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π12 comprehension. (shrink)

Let n be a positive integer. By a $\beta_{n}-model$ we mean an $\omega-model$ which is elementary with respect to $\sigma_{n}^{1}$ formulas. We prove the following $\beta_{n}-model$ version of $G\ddot{o}del's$ Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a $\beta_{n}-model$ of S, then there exists a $\beta_{n}-model$ of S + "there is no countable $\beta_{n}-model$ of S". We also prove a $\beta_{n}-model$ version of $L\ddot{o}b's$ Theorem. As a corollary, we obtain (...) a $\beta_{n}-model$ which is not a $\beta_{n+1}-model$. (shrink)

We study the Lindenbaum algebra ${\fancyscript{A}}$ (WKL o, RCA o) of sentences in the language of second-order arithmetic that imply RCA o and are provable from WKL o. We explore the relationship between ${\Sigma^1_1}$ sentences in ${\fancyscript{A}}$ (WKL o, RCA o) and ${\Pi^0_1}$ classes of subsets of ω. By applying a result of Binns and Simpson (Arch. Math. Logic 43(3), 399–414, 2004) about ${\Pi^0_1}$ classes, we give a specific embedding of the free distributive lattice with countably many generators into ${\fancyscript{A}}$ (...) (WKL o, RCA o). (shrink)

The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the “logical” content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system (...) for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results. (shrink)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle (...) "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA ${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. (...) These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis. (shrink)

We show that \\) cannot be proved with one typical application of \\) in an intuitionistic extension of \ to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach’s axiomatization of higher order reverse mathematics, results related to modified reducibility, and a formalization of Weihrauch reducibility.

Longtermists have argued that humanity should significantly increase its efforts to prevent catastrophes like nuclear wars, pandemics, and AI disasters. But one prominent longtermist argument overshoots this conclusion: the argument also implies that humanity should reduce the risk of existential catastrophe even at extreme cost to the present generation. This overshoot means that democratic governments cannot use the longtermist argument to guide their catastrophe policy. In this paper, we show that the case for preventing catastrophe does not depend on longtermism. (...) Standard cost-benefit analysis implies that governments should spend much more on reducing catastrophic risk. We argue that a government catastrophe policy guided by cost-benefit analysis should be the goal of longtermists in the political sphere. This policy would be democratically acceptable, and it would reduce existential risk by almost as much as a strong longtermist policy. (shrink)

Carl Craver investigates what we are doing when we sue neuroscience to explain what's going on in the brain.

Jung has never pursued the "psychology of religion" apart from general psychology. The unique importance of his work lies rather in his discovery and treatment of religious, or potentially religious, factors in his investigation into the unconscious as a whole and in his general therapeutic practice. In Answer to Job , first published in Zurich in 1952, Jung employs the familiar language of theological discourse. Such terms as "God," "wisdom," and "evil" are the touchstones of his argument. And yet, Answer (...) to Job , perhaps Jung's most controversial work, is not an essay in theology as much as it is an examination of the symbolic role that theological concepts play in a person's psychic life. (shrink)

Carl F. Craver investigates what we are doing when we use neuroscience to explain what's going on in the brain. When does an explanation succeed and when does it fail? Craver offers explicit standards for successful explanation of the workings of the brain, on the basis of a systematic view about what neuroscientific explanations are.

Discrimination, understood as differential treatment of individuals on the basis of their respective group memberships, is widely considered to be morally wrong. This moral judgment is backed in many jurisdictions with the passage of equality of opportunity legislation, which aims to ensure that racial, ethnic, religious, sexual, sexual-orientation, disability and other groups are not subjected to discrimination. This chapter explores the conceptual underpinnings of discrimination and equality of opportunity using the tools of analytical moral and political philosophy.

In this systematic introduction to the philosophy of Charles S. Peirce, the author focuses on four of Peirce's fundamental conceptions: pragmatism and Peirce's development of it into what he called 'pragmaticism'; his theory of signs; his phenomenology; and his theory that continuity is of prime importance for philosophy. He argues that at the centre of Peirce's philosophical project is a unique form of metaphysical realism, whereby continuity and evolutionary change are both necessary for our understanding of experience. In his final (...) chapter Professor Hausman applies this version of realism to contemporary controversies between anti-realists and anti-idealists. Peirce's views are compared to those of such contemporary figures as Davidson, Putnam, and Rorty. The book will be of particular interest to philosophers concerned with American philosophy and current debates on realism as well as linguists working in semiotics. (shrink)

Written three years before his death, The Undiscovered Self combines acuity with concision in masterly fashion and is Jung at his very best. Offering clear and crisp insights into some of his major theories, such as the duality of human nature, the unconscious, human instinct and spirituality, Jung warns against the threats of totalitarianism and political and social propaganda to the free-thinking individual. As timely now as when it was first written, Jung's vision is a salutary reminder of why we (...) should not become passive members of the herd. With a new foreword by Sonu Shamdasani. (shrink)

Under what conditions are people responsible for their choices and the outcomes of those choices? How could such conditions be fostered by liberal societies? Should what people are due as a matter of justice depend on what they are responsible for? For example, how far should healthcare provision depend on patients' past choices? What values would be realized and which hampered by making justice sensitive to responsibility? Would it give people what they deserve? Would it advance or hinder equality? The (...) explosion of philosophical interest in such questions has been fuelled by increased focus on individual responsibility in political debates. Political philosophers, especially egalitarians, have responded to such developments by attempting to map out the proper place for responsibility in theories of justice. This book both reflects on these recent developments in normative political theory and moves the debate forwards. (shrink)

One of the most significant political philosophers of the twentieth century, Carl Schmitt is a deeply controversial figure who has been labeled both Nazi sympathizer and modern-day Thomas Hobbes. First published in 1938, The Leviathan in the State Theory of Thomas Hobbes used the Enlightenment philosopher’s enduring symbol of the protective Leviathan to address the nature of modern statehood. A work that predicted the demise of the Third Reich and that still holds relevance in today’s security-obsessed society, this volume (...) will be essential reading for students and scholars of political science. “Carl Schmitt is surely the most controversial German political and legal philosopher of this century. . . . We deal with Schmitt, against all odds, because history stubbornly persists in proving many of his tenets right.”— Perspectives on Political Science “[A] significant contribution. . . . The relation between Hobbes and Schmitt is one of the most important questions surrounding Schmitt: it includes a distinct, though occasionally vacillating, personal identification as well as an association of ideas.”— Telos. (shrink)

This introductory chapter provides an overview of the recent debate about responsibility and distributive justice. It traces the recent philosophical focus on distributive justice to John Rawls and examines two arguments in his work which might be taken to contain the seeds of the focus on responsibility in later theories of distributive justice. It examines Ronald Dworkin's ‘equality of resources’, the ‘luck egalitarianism’ of Richard Arneson and G. A. Cohen, as well as the criticisms of their work put forward by (...) Elizabeth Anderson, Marc Fleurbaey, Susan Hurley, and Jonathan Wolff. Key concepts such as responsibility (individual and collective), luck (thin and thick; brute and option), control, desert, and equality of opportunity are delineated, and the implementation of responsibility-sensitive accounts of justice is considered. The chapters of this book are positioned in relation to the wider literature on responsibility and distributive justice, and a brief outline of the chapters is provided. (shrink)

In this paper I argue against one variety of contextualism about aesthetic predicates such as “beautiful.” Contextualist analyses of these and other predicates have been subject to several challenges surrounding disagreement. Focusing on one kind of contextualism— individualized indexical contextualism —I unpack these various challenges and consider the responses available to the contextualist. The three responses I consider are as follows: giving an alternative analysis of the concept of disagreement ; claiming that speakers suffer from semantic blindness; and claiming that (...) attributions of beauty carry presuppositions of commonality. I will argue that none of the available strategies gives a response which both satisfactorily explains all of the disagreement -data and is plausible independent of significant evidence in favor of contextualism. I conclude that individualized indexical contextualism about the aesthetic is untenable, although this does not rule out alternative contextualist approaches to the aesthetic. (shrink)

Traces the development of the integral and the differential calculus and related theories since ancient times.

This chapter identifies three contrasts between responsibility-sensitive justice and desert-sensitive justice. First, while responsibility may be appraised on prudential or moral grounds, it is argued that desert is necessarily moral. As moral appraisal is much more plausible, responsibility-sensitive justice is only attractive in one of its two formulations. Second, strict responsibility sensitivity does not compensate for all forms of bad brute luck, and forms of responsibility-sensitive justice like luck egalitarianism that provide such compensation do so by appealing to independent moral (...) concerns such as equality. Desert-sensitive justice can deliver the appropriate compensation without relying on external moral resources. Finally, while responsibility-sensitive justice harshly refuses to provide for those whose basic needs are unsatisfied due to their own negligent actions, this result can be averted by desert-sensitive justice as it can take into account responsibility-independent considerations. In sum, desert-sensitive justice appears to offer a tighter fit with considered judgments about justice. (shrink)

With a characteristically broad and provocative treatment, Dahlhaus examines a single music-aesthetical idea from various historical and philosophical viewpoints. "Essential reading for anyone interested in the larger intellectual framework in which Romantic music found its place, a framework that to a remarkable degree has continued to shape our image of music."--Robert P. Morgan, Yale University Carl Dahlhaus (1928-1989) is the author of a highly influential body of works on the foundations of music history and aesthetics.

This collection of articles and associated discussion papers focuses on a problem that has attracted increasing attention from linguists and psychologists throughout the world during the past several years. Reduced to essentials, the problem is that of discovering the character of the mental capacities that make it possible for human beings to attain knowledge of their language on the basis of fragmentary and haphazard early linguistic experience. A fundamental assumption running through all of these contributions is that people possess strong (...) innate predispositions that are critical for success in this task. (shrink)

According to one large family of views, scientific explanations explain a phenomenon (such as an event or a regularity) by subsuming it under a general representation, model, prototype, or schema (see Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441; Churchland, P. M. (1989). A neurocomputational perspective: The nature of mind and the structure of science. Cambridge: MIT Press; Darden (2006); Hempel, C. G. (1965). Aspects of scientific (...) explanation. In C. G. Hempel (Ed.), Aspects of scientific explanation (pp. 331–496). New York: Free Press; Kitcher (1989); Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25). My concern is with the minimal suggestion that an adequate philosophical theory of scientific explanation can limit its attention to the format or structure with which theories are represented. The representational subsumption view is a plausible hypothesis about the psychology of understanding. It is also a plausible claim about how scientists present their knowledge to the world. However, one cannot address the central questions for a philosophical theory of scientific explanation without turning one’s attention from the structure of representations to the basic commitments about the worldly structures that plausibly count as explanatory. A philosophical theory of scientific explanation should achieve two goals. The first is explanatory demarcation. It should show how explanation relates with other scientific achievements, such as control, description, measurement, prediction, and taxonomy. The second is explanatory normativity. It should say when putative explanations succeed and fail. One cannot achieve these goals without undertaking commitments about the kinds of ontic structures that plausibly count as explanatory. Representations convey explanatory information about a phenomenon when and only when they describe the ontic explanations for those phenomena. (shrink)

A core, constitutive norm of science is to remove or remedy the artefacts in one’s data. Here, we consider examples of artefacts from many fields of science (for example, astronomy, economics, electrophysiology, psychology, and systems neuroscience) and discuss their contribution to a more general evidential selection problem at the heart of the epistemology of evidence. Synthesizing and building on previously disparate discussions in many areas of the philosophy of science, we provide a novel, causal–pragmatic account that fits the examples and (...) clarifies the practices by which artefacts are discovered and remedied. (shrink)

This work presents a dialogue between classical and contemporary Indian and postmodern thinkers. Juxtaposing the diverse perspectives of Indian philosophers and philosophies, including Buddhism, Sankara, and Radhakrishnan, and western postmodern thinkers such as Lacan and Derrida, Olson addresses topics such as desire, suffering, the self, and identity.

_Black Intellectual Thought in Education_ celebrates the exceptional academic contributions of African-American education scholars Anna Julia Cooper, Carter G. Woodson, and Alain Leroy Locke to the causes of social science, education, and democracy in America. By focusing on the lives and projects of these three figures specifically, it offers a powerful counter-narrative to the dominant, established discourse in education and critical social theory--helping to better serve the population that critical theory seeks to advocate. Rather than attempting to "rescue" a few (...) African American scholars from obscurity or marginalization, this powerful volume instead highlights ideas that must be probed and critically examined in order to deal with prevailing contemporary educational issues. Cooper, Woodson, and Locke’s history of engagement with race, democracy, education, gender and life is a dynamic, demanding, and authentic narrative for those engaged with these important issues. (shrink)

The Proliferation of Rights explores how the assertion of rights has expanded dramatically since World War II. Carl Wellman illuminates for the reader the historical developments in each of the major categories of rights, including human rights, civil rights, women’s rights, patient rights, and animal rights. He concludes by assessing where this proliferation has been legitimate and helpful, cases where it has been illusory and unproductive, and alternatives to the appeal to rights.

We argue that intelligible appeals to interlevel causes (top-down and bottom-up) can be understood, without remainder, as appeals to mechanistically mediated effects. Mechanistically mediated effects are hybrids of causal and constitutive relations, where the causal relations are exclusively intralevel. The idea of causation would have to stretch to the breaking point to accommodate interlevel causes. The notion of a mechanistically mediated effect is preferable because it can do all of the required work without appealing to mysterious interlevel causes. When interlevel (...) causes can be translated into mechanistically mediated effects, the posited relationship is intelligible and should raise no special philosophical objections. When they cannot, they are suspect. (shrink)

Here a distinguished American historian challenges the belief that the eighteenth century was essentially modern in its temper. In crystalline prose Carl Becker demonstrates that the period commonly described as the Age of Reason was, in fact, very far from that; that Voltaire, Hume, Diderot, and Locke were living in a medieval world, and that these philosophers “demolished the Heavenly City of St. Augustine only to rebuild it with more up-to-date materials.” In a new foreword, Johnson Kent Wright looks (...) at the book’s continuing relevance within the context of current discussion about the Enlightenment. “Will remain a classic—a beautifully finished literary product.”—Charles A. Beard, _American Historical Review_ “_The Heavenly City of the Eighteenth-Century Philosophers _remains_ _one of the most distinctive American contributions to the historical literature on the Enlightenment.... [It] is likely to beguile and provoke readers for a long time to come.”—Johnson Kent Wright, from the foreword. (shrink)

This paper develops a theory of how democratic governance is possible. It analyses democracy as a laminated system consisting of three interdependent levels – the political/institutional, the socia...

Not all models are explanatory. Some models are data summaries. Some models sketch explanations but leave crucial details unspecified or hidden behind filler terms. Some models are used to conjecture a how-possibly explanation without regard to whether it is a how-actually explanation. I use the Hodgkin and Huxley model of the action potential to illustrate these ways that models can be useful without explaining. I then use the subsequent development of the explanation of the action potential to show what is (...) required of an adequate mechanistic model. Mechanistic models are explanatory. (shrink)

This chapter focuses on an explanation of the neglect of investigating and understanding emotional response to films. It argues that the kind of emotional experience a film offers is a proper target of ideological investigation. This chapter aims to suggest how emotions should be understood in ideological criticism. There is characterization of spectator emotion with a view toward conceptual clarification. This chapter examines two families of screen emotions: sentiment and sentimentality, and the emotions which accompany screen violence. Drawing on work (...) in both cognitive science and recent philosophy of mind, the chapter argues that a cognitive approach to the emotions offers a way of taking the role of emotions more seriously than it has been taken in most contemporary film theory. The chapter's usage of ‘cognitivism’ is distinctive by virtue of its challenge to the traditional distinction between reason and passion. (shrink)

Some philosophers writing on the possibility of faultless disagreement have argued that the only way to account for the intuition that there could be disagreements which are faultless in every sense is to accept a relativistic semantics. In this article we demonstrate that this view is mistaken by constructing an absolutist semantics for a particular domain – aesthetic discourse – which allows for the possibility of genuinely faultless disagreements. We argue that this position is an improvement over previous absolutist responses (...) to the relativist's challenge and that it presents an independently plausible account of the semantics of aesthetic discourse. (shrink)

Many areas of science develop by discovering mechanisms and role functions. Cummins' (1975) analysis of role functions-according to which an item's role function is a capacity of that item that appears in an analytic explanation of the capacity of some containing system-captures one important sense of "function" in the biological sciences and elsewhere. Here I synthesize Cummins' account with recent work on mechanisms and causal/mechanical explanation. The synthesis produces an analysis of specifically mechanistic role functions, one that uses the characteristic (...) active, spatial, temporal, and hierarchical organization of mechanisms to add precision and content to Cummins' original suggestion. This synthesis also shows why the discovery of role functions is a scientific achievement. Discovering a role function (i) contributes to the interlevel integration of multilevel mechanisms, and (ii) provides a unique, contextual variety of causal/mechanical explanation. (shrink)

This book offers a bold new theoretical understanding of the current ecological crisis via the Frankfurt School. Focusing on key notions of dialectics, natural history, and materialism, a critical theory of nature is outlined in favor of a more traditional Marxist theory of nature, albeit one which still builds on Marxist concepts to confirm humanity's centrality in manufacturing environmental misery. Pre-eminent thinkers including Georg Lukács, Ernst Bloch, and Theodor Adorno are highlighted for their potential to diagnose the interpenetration of capitalism (...) and nature in a way that neither absolutizes nor obliterates the boundary between the social and natural. (shrink)